Search for variation of the fine-structure constant using optical clock transitions in Cf$^{15+}$, Es$^{17+}$ and Es$^{16+}$ ions

We study optical transitions in Cf$^{15+}$, Es$^{17+}$ and Es$^{16+}$ ions using the high-precision relativistic method that combines the configuration interaction and linearized coupled-cluster approaches. We identify the transitions that are extremely sensitive to the variation of the fine-structure constant. The sensitivities are the largest among all atomic systems studied so far. These transitions have all features for the implementation of the ultra-precision optical atomic clocks for test of the $\alpha$-variation at extremely high accuracy of 10$^{-20}$ per year.